Theoretical physics: The origins of space and time

12/24/2014

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Many researchers believe that physics will not be complete
until it can explain not just the behavior of space and time, but where these
entities come from. “Imagine waking up one day and realizing that you actually
live inside a computer game,” says Mark Van Raamsdonk, describing what sounds
like a pitch for a science-fiction film. But for Van Raamsdonk, a physicist at
the University of British Columbia in Vancouver, Canada, this scenario is a way
to think about reality. If it is true, he says, “everything around us — the
whole three-dimensional physical world — is an illusion born from information
encoded elsewhere, on a two-dimensional chip”. That would make our Universe,
with its three spatial dimensions, a kind of hologram, projected from a
substrate that exists only in lower dimensions.

This ‘holographic principle’ is strange even by the usual
standards of theoretical physics. But Van Raamsdonk is one of a small band of
researchers who think that the usual ideas are not yet strange enough. If
nothing else, they say, neither of the two great pillars of modern physics —
general relativity, which describes gravity as a curvature of space and time,
and quantum mechanics, which governs the atomic realm — gives any account for
the existence of space and time. Neither does string theory, which describes
elementary threads of energy. Van Raamsdonk and his colleagues are convinced that physics
will not be complete until it can explain how space and time emerge from
something more fundamental — a project that will require concepts at least as
audacious as holography.

They argue that such a radical reconceptualization of
reality is the only way to explain what happens when the infinitely dense
‘singularity’ at the core of a black hole distorts the fabric of space-time
beyond all recognition, or how researchers can unify atomic-level quantum
theory and planet-level general relativity — a project that has resisted theorists’
efforts for generations. “All our experiences tell us we shouldn’t have two
dramatically different conceptions of reality — there must be one huge
overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State
University in University Park.

Finding that one huge theory is a daunting challenge. Here,
Nature explores some promising lines of attack — as well as some of the
emerging ideas about how to test these concepts (see ‘The fabric of reality’).

Gravity
as thermodynamics

One of the most obvious questions to ask is whether this
endeavour is a fool’s errand. Where is the evidence that there actually is
anything more fundamental than space and time?

A provocative hint comes from a series of startling
discoveries made in the early 1970s, when it became clear that quantum
mechanics and gravity were intimately intertwined with thermodynamics, the
science of heat.

In 1974, most famously, Stephen Hawking of the University of
Cambridge, UK, showed that quantum effects in the space around a black hole
will cause it to spew out radiation as if it was hot. Other physicists quickly
determined that this phenomenon was quite general. Even in completely empty
space, they found, an astronaut undergoing acceleration would perceive that he
or she was surrounded by a heat bath. The effect would be too small to be
perceptible for any acceleration achievable by rockets, but it seemed to be
fundamental. If quantum theory and general relativity are correct — and both
have been abundantly corroborated by experiment — then the existence of Hawking
radiation seemed inescapable.

A second key discovery was closely related. In standard
thermodynamics, an object can radiate heat only by decreasing its entropy, a
measure of the number of quantum states inside it. And so it is with black
holes: even before Hawking’s 1974 paper, Jacob Bekenstein, now at the Hebrew
University of Jerusalem, had shown that black holes possess entropy. But there
was a difference. In most objects, the entropy is proportional to the number of
atoms the object contains, and thus to its volume. But a black hole’s entropy
turned out to be proportional to the surface area of its event horizon — the
boundary out of which not even light can escape. It was as if that surface somehow
encoded information about what was inside, just as a two-dimensional hologram
encodes a three-dimensional image.

In 1995, Ted Jacobson, a physicist at the University of
Maryland in College Park, combined these two findings, and postulated that every
point in space lies on a tiny ‘black-hole horizon’ that also obeys the
entropy–area relationship. From that, he found, the mathematics yielded
Einstein’s equations of general relativity — but using only thermodynamic
concepts, not the idea of bending space-time .

“This seemed to say something deep about the origins of
gravity,” says Jacobson. In particular, the laws of thermodynamics are
statistical in nature — a macroscopic average over the motions of myriad atoms
and molecules — so his result suggested that gravity is also statistical, a
macroscopic approximation to the unseen constituents of space and time.

In 2010, this idea was taken a step further by Erik
Verlinde, a string theorist at the University of Amsterdam, who showed that
the statistical thermodynamics of the space-time constituents — whatever they
turned out to be — could automatically generate Newton’s law of gravitational
attraction.

And in separate work, Thanu Padmanabhan, a cosmologist at
the Inter-University Centre for Astronomy and Astrophysics in Pune, India,
showed that Einstein’s equations can be rewritten in a form that makes them
identical to the laws of thermodynamics — as can many alternative theories of
gravity. Padmanabhan is currently extending the thermodynamic approach in an
effort to explain the origin and magnitude of dark energy: a mysterious cosmic
force that is accelerating the Universe’s expansion.

Testing such ideas empirically will be extremely difficult.
In the same way that water looks perfectly smooth and fluid until it is
observed on the scale of its molecules — a fraction of a nanometre — estimates
suggest that space-time will look continuous all the way down to the Planck
scale: roughly 10−35 metres, or some 20 orders of magnitude smaller than a
proton.

But it may not be impossible. One often-mentioned way to
test whether space-time is made of discrete constituents is to look for delays
as high-energy photons travel to Earth from distant cosmic events such as
supernovae and γ-ray bursts. In effect, the shortest-wavelength photons would
sense the discreteness as a subtle bumpiness in the road they had to travel,
which would slow them down ever so slightly. Giovanni Amelino-Camelia, a
quantum-gravity researcher at the University of Rome, and his colleagues have
found hints of just such delays in the photons from a γ-ray burst recorded in
April. The results are not definitive, says Amelino-Camelia, but the group
plans to expand its search to look at the travel times of high-energy neutrinos
produced by cosmic events. He says that if theories cannot be tested, “then to
me, they are not science. They are just religious beliefs, and they hold no interest
for me.”

Other physicists are looking at laboratory tests. In 2012,
for example, researchers from the University of Vienna and Imperial College
London proposed a tabletop experiment in which a microscopic mirror would be
moved around with lasers. They argued that Planck-scale granularities in
space-time would produce detectable changes in the light reflected from the
mirror (see Nature http://doi.org/njf; 2012).

Loop
quantum gravity

Even if it is correct, the thermodynamic approach says
nothing about what the fundamental constituents of space and time might be. If
space-time is a fabric, so to speak, then what are its threads? One possible
answer is quite literal. The theory of loop quantum gravity, which has been
under development since the mid-1980s by Ashtekar and others, describes the
fabric of space-time as an evolving spider’s web of strands that carry
information about the quantized areas and volumes of the regions they pass
through . The individual strands of the web must eventually join their ends to
form loops — hence the theory’s name — but have nothing to do with the much
better-known strings of string theory. The latter move around in space-time,
whereas strands actually are space-time: the information they carry defines the
shape of the space-time fabric in their vicinity.

Because the loops are quantum objects, however, they also
define a minimum unit of area in much the same way that ordinary quantum
mechanics defines a minimum ground-state energy for an electron in a hydrogen
atom. This quantum of area is a patch roughly one Planck scale on a side. Try
to insert an extra strand that carries less area, and it will simply disconnect
from the rest of the web. It will not be able to link to anything else, and
will effectively drop out of space-time.